Enerji İletiminde Gerilim Kararlı En Uygun Reaktif Güç Desteklemelerinin İncelenmesi

Abstract

Elektriksel güç, ekonomik ve çevresel nedenler yüzünden uzun mesafelere iletildiği için son yulardaki ilgi, gerilim kararlılığı üzerinde yoğunlaşmıştır. Bu bağlamda, gerilim kararlılığı tüm işletim koşullan altında sürekli halde belirlenen işletim limitlerindeki yük gerilim genliklerinin kararlılığını muhafaza etmek amacıyla, yeterli reaktif güç beslemesini, sistemin sağlama kabiliyeti olarak verilebilir. Bu çalışmada ilk olarak, gerilim kararlılığı konusu, hat kayıplarının, paralel hat sayısının, hat başı geriliminin, güç katsayısının, hat uzunluğunun, reaktif güç kompanzasyonunun, seri ve şönt kompanzasyonun hat sonu kritik değerleri üzerindeki etkileri, radyal hat için analitik ifadeler kullanarak incelenmiştir. Sonuçlar grafikler halinde verilmiştir. Hat kompanzasyonunun çeşitli biçimlerini de göz önüne almak için incelemeler altı farklı iletim modeli için yapılmıştır. Daha sonra 21 baralı bir örnek sistem ele alınmış ve yük akışı hesaplamaları kullanılarak gerilim kararlılığı, örnek sistem besleme hatlarının çeşitli durumları için incelenmiştir, örnek sistem içinde muhtelif tipte beş adet bara göz önüne alınarak, bu haralarda yapılan reaktif güç kompanzasyonunun gerilim kararlılığı üzerindeki etkisi araştırılmıştır. Gerilim kararsızlığının başlıca nedeni yeterli reaktif güç verilememesi olduğu için çalışmada reaktif güç yerleşimi için uygun haraların belirlenmesi konusu da incelenmiştir. İncelemelerde ayrık (decoupled) yük akışı jacobian matrisi ve V-Q duyarlılık matrisi kullanılarak, kararlılık iyileştirici reaktif güç yerleştirmesi için bara sıralamaları oluşturulmuştur. 21 baralı örnek sistem üzerinde hesaplanan kritik reaktif güç değerlerinden elde edilen sıralama ile bu iki duyarlılık yaklaşımı karşılaştmlmıştır. Ayrıca haraların belirlenmesinde kararlılığın iyileştirilmesinin yanı sıra aktif güç kaybının azaltılması ve iyi bir gerilim kontrolünün de sağlanması düşüncesi ile duyarlılık ilişkilerinden bu iki amaç için de bara sıralamaları elde edilmiştir. Tüm sıralamaları bir arada düşünerek reaktif güç yerleşimi için son bara sıralaması, iki yöntemle elde edilmiştir. Yöntemlerden birincisi haralara ağırlık faktörleri vermektir, diğeri ise farklı bir yaklaşım olarak bulanık karar verme (füzzy decision making) yöntemidir.

The planning, operation and control of a power system are to a significant extent governed by stability consideration. Power system stability may be broadly defined as that property of a power system that enables it to remain in a state of operating equilibrium under normal operating conditions and to regain an acceptable state of equilibrium after being subjected to a disturbance. Transient ör steady-state stability of power system is its capability to operate stable without loss of synchronism after a large ör small disturbance respectively. Voltage stability, on the other hand, is the ability of the system to provide adequate reactive power support under ali operating conditions so as to maintain stable load voltage magnitudes with in specified operating limits in the steady-state. Voltage control and stability problems are not new to the electric utility industry but are now receiving special attention in many systems. Önce associated primarily with weak systems and long lines, voltage problems are now also a source of concern in highly developed networks as a result of heavier loading. Voltage instability is essentially a local phenomenon; however, its consequences may have a widespread impact. Voltage collapse is more complex than simple voltage instability and is usuaÜy the result of a sequence of events accompanying voltage instability leading to a low- voltage profile in a significant part of the power system. Voltage stability problems normally occur in heavily stressed systems. While the disturbance leading to voltage collapse may be initiated by a variety of causes, the underlying problem is an inherent weakness in the power system. in addition to the strength of transmission netvvork and power transfer levels, the principal factors, contributing to voltage collapse are the generator reactive power/voltage control limits, load characteristics, characteristics of reactive compensation devices, and the action of voltage control devices such as transformer under-load tap changers (ULTCs). The methods for predicting voltage collapse can be divided into either steady state (static) ör dynamic methods. The steady state methods can be subdivided into those related to the existence of an acceptable voltage profile across the netvvork (Load Flovv Feasibility Methods) and those which test for the existence of a stable equüibrium point of the povver system (Steady-State Stability Methods). XX \/ . _.. 4_ Critical Vrcrt tpolnt _^=^L jj ! ^ l Prcrt Figüre l PV curve. Voltage stability, in fact, depends on the relationships between P,Q and V. The characteristics which show the relationships betvveen the transmitted power (Pr), receiving end voltage (Vr), and the reactive power injection (Qj) are used to analysis voltage stability. A PV curve is shown in figüre 1. Only the operating points above the critical point represent satisfactory operating conditions. PV curve ( ör QV curve) and critical values can be calculated by analytical for radial systems. But, for complex systems with a large number of voltage sources and load buses, these characteristics can be determined by using power-flow analysis. There are a few possibilities for control when the system is approaching voltage stability boundary : some of the reported control actions include increasing reactive generation until maximum reactive generation capability and/or satisfactory system conditions are reached, freezing the operation of under-load tap-changing transformers, lowering voltages in the distribution netvvork, and even performing load shedding in extreme situations. in a electric power system, VAr reserves should be allocated in such a way that the system does not move towards voltage collapse (VC) as the system demand changes. Qdistto VC ; maximum increase of reactive demand at the node that the system can vvithstand before it becomes voltage unstable. Voltage collapse condition, defined for any node in the power system are depicted in figüre 2. The shape of the QV curve for a given node is defined by the characteristics and loading conditions of the transmission facilities between the sources of reactive power and node i. A sensitivity calculation can be performed to find a strategy to increase reactive power reserves where an increase in reactive reserves is required. xxi give information about the voltage variation at bus j, if reactive power at bus i is changed. The location of the reactive power device for voltage control should be decided in such a way that the result affects as many buses as possible. For this a voltage performance index (V.P.I) is defined as follows: (V.P.IJ-CNORMX-CaX (7) where ( V. P. I); voltage performance index for the ith bus (NORM). norm of the ith column of matrix Jv (a)j standard deviation of the elements of ith column around the average value, i load buses The reactive device locations are ordered based on the above index. The higher the value of ( V.P.I); the better is its voltage control capability. To obtain final ordering for the reactive power location, two method can be used. First method is to use weight factors, second method is to use fuzzy decision making which is a different way. In the first method, the load buses are given weight factors according to its order for every index. Final ordering can be obtained by summing weight factors for each bus and than by ordering the load buses according to decreasing total weight value. Decision making is defined to include any choice or selection alternatives. Applications of fuzzy sets within the field of decision making have, for the most part, consisted of extensions or fuzzifications of the classical theories of decision making. A fuzzy model of group decision was proposed by Blin (1974) and Blin and Whinston (1973). Here, each member of a group of n individual decision makers is assumed to have a reflexive, antisymmetric, and transitive preference ordering Pk, keNn, which totally or partially orders a set X of alternatives. A social choice function must then be found which, given the individual preference orderings, produces the most acceptable overall group preference ordering. Basically, this model allows for the individual decision makers to possess different aims and values while still assuming that the overall purpose is to reach a common, acceptable decision. In order to deal with the multiplicity of opinion evidenced in the group, the social preference S may be defined as a fuzzy binary relation with membership grade function Hs:XxX->[0,l] (8) XXIV AQ = JR.AV (2) where JR=J4-J3.J-'.J2 (3) and JR is the reduced jacobian matrk of the system. From equation (2), we may write AV = JR'.AQ (4) The matrix JR is the reduced V-Q jacobian. Its i' th diagonal elements is the V-Q sensitivity at bus i. The V-Q sensitivity at a bus represents the slope of the Q-V curve at the given operating point. A positive V-Q sensitivity is indicative of stable operation; the sınailer the sensitivity, the more stable the system. As stability decreases, the magnitude of the sensitivity increases, becoming infinite at the stability limit. Conversly, a negative V-Q sensitivity is indicative of unstable operation. Therefore if load buses are ordered according to decreasing magnitude of diagonal J J^1 elements for a stable operation condition, the order of candidate buses for location can be obtain. There are effects of reactive power variation at the load buses on system losses. For a small change in reactive power, there is a linear relationship betvveen reactive power and total power loss, [APL] = [^][AQL] (5) where subscript L indicates that only load buses are considered. Therefore, we can obtain candidate buses for locating reactive power compensation by ordering the load buses according to the magnitude of--. ^VL The main objective of reactive power control is to maintain a desired voltage profile on the system. The expression for change in voltage (AV) in terms of change in reactive power (AQ) is, [AVL] = [JV].[AQL] (6) Here the diagonal elements of Jy, i.e. Jjj give information about the voltage variation at bus i, if the reactive power at the same bus is changed. Off diagonal elements Jyjj xxiii give information about the voltage variation at bus j, if reactive power at bus i is changed. The location of the reactive power device for voltage control should be decided in such a way that the result affects as many buses as possible. For this a voltage performance index (V.P.I) is defined as follows: (V.P.IJ-CNORMX-CaX (7) where ( V. P. I); voltage performance index for the ith bus (NORM). norm of the ith column of matrix Jv (a)j standard deviation of the elements of ith column around the average value, i load buses The reactive device locations are ordered based on the above index. The higher the value of ( V.P.I); the better is its voltage control capability. To obtain final ordering for the reactive power location, two method can be used. First method is to use weight factors, second method is to use fuzzy decision making which is a different way. In the first method, the load buses are given weight factors according to its order for every index. Final ordering can be obtained by summing weight factors for each bus and than by ordering the load buses according to decreasing total weight value. Decision making is defined to include any choice or selection alternatives. Applications of fuzzy sets within the field of decision making have, for the most part, consisted of extensions or fuzzifications of the classical theories of decision making. A fuzzy model of group decision was proposed by Blin (1974) and Blin and Whinston (1973). Here, each member of a group of n individual decision makers is assumed to have a reflexive, antisymmetric, and transitive preference ordering Pk, keNn, which totally or partially orders a set X of alternatives. A social choice function must then be found which, given the individual preference orderings, produces the most acceptable overall group preference ordering. Basically, this model allows for the individual decision makers to possess different aims and values while still assuming that the overall purpose is to reach a common, acceptable decision. In order to deal with the multiplicity of opinion evidenced in the group, the social preference S may be defined as a fuzzy binary relation with membership grade function Hs:XxX->[0,l] (8) XXIV which assigns the membership grade jj.s(xi,xj) indicating the degree of group preference of alternative xj, over alternative xj. The expression of this group preference requires some appropriate means of aggregating the individual preferences. One simple method computes the relative popularity of alternative xj over xj by dividing the number of persons preferring xj to xj, denoted by N(xj,xj), by the total number of decision makers, n. This scheme corresponds to the simple majority vote. Thus, / \ NCx^Xj) us(xiîXjJ = - (9) once the fuzzy relationship S has been defined, the final nonfuzzy group preference can be determined by converting S into its resolution form S = U«Sa (10) a which is the union of the crisp relation Sa comprising the a-cuts of the fuzzy relation S, aeAs (the level set of S), each scaled by a. Each value a essentially represents the level of agreement between the individuals concerning the particular crisp ordering Sa. One procedure that maximizes the final agreement level consist of intersecting the classes of crisp total orderings that are compatible with the pairs in the a-cuts Sa for increasingly smaller values of a until a single crisp total ordering is achieved. In this process, any pairs (x{,xj) that lead to an intransitivity are removed. The largest value a for which the unique compatible ordering on XxX is found represents the maximized agreement level of the group and the crisp ordering itself represents the group decision. In this study, first the critical values are calculated on a two-bus (radial) system with six different compensation models for different operating conditions which are obtained by changing the sending end voltage magnitude, line loss factor, load power factor, length of üne, number of line, the degree of series and shunt compensation. Hence, the model 5 can be observed as better transmission line model. Then, an example system with 5 generator buses and 16 load buses is considered. For different types of the system buses, the effects of the reactive compensation to the critical values of the buses are studied. Furthermore, the candidate buses are determined to locate reactive power device by using sensitivity relationships according to steady-state stability, real power loss, voltage control. Final ordering of the buses are obtained by using weight factors and fuzzy decision making which is considered as a different method. As a result, reactive power should be generated as near as possible at consumption centers. To improve voltage control capacity of the system, reactive power devices which have fast control times should be located at the buses at which many lines are connected. In order to be able to consider multi-objective view in VAr compensator placement, fuzzy decision making method can be used.